JPH10126113A - Automatic tuning method for microwave circuit - Google Patents

Abstract

PROBLEM TO BE SOLVED: To quickly obtain a proper initial position of an E-plane stub and an H-plane stub with which the impedance of the microwave circuit is matched. SOLUTION: Absolute value and the phase of a reflection coefficient, when both an E-plane stub and an H-plane stub are at a position mated to an inner face of a square waveguide (stub reference position) are measured (S4). A proper position of each stub is calculated based on the absolute value and its phase of the reflection coefficient (S6), and each stub is moved to the position (S7). When a load suddenly fluctuated, the absolute value and the phase of the reflection coefficient after the fluctuation are measured to calculated the absolute value and its phase of the reflection coefficient when each stub is at the stub reference position based on the measured values, thereby obtaining a proper position for each stub.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for automatically tuning a microwave circuit for supplying microwave power to a load such as a plasma generator.

[0002]

2. Description of the Related Art As a conventional automatic tuning method for a microwave circuit of this kind, a method using a stub matching device as described below is known. This stub matching device is provided in the middle of a rectangular waveguide connecting the microwave generator and the load,
There is provided a branch pipe which is branched from two adjacent surfaces of the rectangular waveguide and has a cross section of substantially the same shape and size as the waveguide. Short-circuit plates are slidably inserted into these branch pipes. The short-circuit plate provided at right angles to the direction of the electric field in the waveguide is E
A plane stub, a short-circuit plate provided at right angles to the magnetic field direction, is also called an H-plane stub. By appropriately adjusting the positions of the E-plane stub and the H-plane stub in the two branch pipes, impedance matching between the microwave generator and the load (hereinafter, also simply referred to as matching) can be achieved.

By the way, it is known that the combination of the positions of the E-plane stub and the H-plane stub changes the impedance of the microwave generator viewed from the load side in a complicated manner. This is schematically shown in FIG. In FIG. 17, the horizontal axis indicates the positions of the E-plane stub and the H-plane stub, and the vertical axis indicates the reflection coefficient. In addition, E side stub and H
Since each position of the surface stub changes independently, the change of the reflection coefficient is three-dimensional, but is shown two-dimensionally for simplicity.

As can be seen from FIG. 17, a plurality of minimum values of the reflection coefficient generally exist in accordance with the combination of the positions of the stubs on the E plane and the H plane. Needless to say, the position P _A where the reflection coefficient is minimum is the point where the microwave generator is matched with the load. That is the target of auto-tuning to automatically set the E-plane stubs and H-plane stubs in this position P _A. If, if within the scope of the E surfaces, regions sandwiching each stub position P _A of the H-plane A, using, for example, well-known feedback control, it is easy to Yuku close each stub at the position P _A. However, each stub is at position P _A
If the no example in the range of the area B included in the normal control, the stub position P _B that takes a minimum value in the region B
And impedance cannot be matched.

[0005] For this reason, in automatic tuning of a microwave circuit, the reflection coefficient takes a minimum value in E.
It is important to know in advance the approximate initial positions of the stubs on the plane and the H plane. Therefore, the applicant of the present application has disclosed in
No. 153599 proposes a method for knowing an appropriate initial position of each stub. The following briefly describes this technique.

First, the relationship between the position of each stub on the E-plane and the H-plane and the reflected power is measured according to the arbitrarily determined waveguide length, incident power, load, etc., and the reflection coefficient is determined from the measurement result. A table map showing the relationship between the position of each stub and the reflection coefficient is calculated in advance. Then, when power is supplied to the load, an initial position of each stub giving a desired reflection coefficient is obtained by referring to the table map, and each stub is moved to that position.

According to this method, there is an advantage that the optimum initial position of each stub can be obtained quickly without repeating trial and error by referring to the table map.

[0008]

As described above, Japanese Patent Application Laid-Open No.
Although the technique disclosed in JP-153599 is useful, the following problems have been clarified. That is, since the above table map needs to be created according to the length of the waveguide, the incident power, the load, and the like, it takes a considerable time to create the table map.

When the impedance of the load suddenly changes due to an external factor, a sharp change appears in the reflection coefficient distribution shown in FIG. That is, the position of each stub on the E-plane and the H-plane that gives the minimum reflection coefficient changes rapidly. As a result, the currently set positions of the stubs on the E-plane and the H-plane greatly deviate from appropriate positions giving the minimum reflection coefficient, and cannot be followed by ordinary control.

The present invention has been made in view of such circumstances, and an automatic tuning method of a microwave circuit capable of easily and quickly obtaining appropriate initial positions of an E-plane stub and an H-plane stub is provided. The purpose is to provide. Another object of the present invention is to provide a method for automatically tuning a microwave circuit, which can move each stub to an appropriate position even if the impedance of a load changes rapidly during supply of microwave power. Is to provide.

[0011]

[Means for Solving the Problems]

[Procedure leading to the present invention] For understanding of the present invention, first, the course leading to the present invention will be described. When the E-plane stub and the H-plane stub of the stub matching device provided in the middle of the rectangular waveguide connecting the microwave generator and the load are displaced, the load including the stub matching device is reduced. How the impedance on the side changes on the Smith chart was examined. Hereinafter, description will be made with reference to the drawings.

FIG. 2 is an external perspective view of a stub matching device provided in a rectangular waveguide, and FIG. 3 is a cross-sectional view thereof. Stub matching devices 2 _E and 2 _H are respectively provided on two orthogonal wall surfaces of the rectangular waveguide 1. Each of the stub matching devices 2 _E and 2 _H has a branch tube 3 _E and a branch tube 3 _E having the same cross-sectional shape as the rectangular waveguide 1.
In 3 _H, stub 4 _E, 4 _H as short-circuiting plate is inserted slidably, respectively. In particular, called the E face stub stubs 4 _E having a surface perpendicular to the electric field direction, the stub 4 _H having a magnetic field parallel to the plane and H-plane stubs. Although not shown, the stubs 4 _E and 4 _H can be set to move to arbitrary positions in the branch pipes 3 _E and 3 _H by a screw feed mechanism driven by a stepping motor. In this example, each of the stubs 4 _E and 4 _H can move up to 39 mm from the position flush with the inner surface of the rectangular waveguide 1 toward the far side of each of the branch pipes 3 _E and 3 _H. . In the present specification, a position where the stubs 4 _E and 4 _H are flush with the inner surface of the rectangular waveguide 1 is called a stub reference position.

The impedance is measured by the stub matching unit 2
_E, the 2 _H position of a little more microwave generators than the installation position of, by detecting a voltage standing wave by installing at least three probes (antenna), the absolute value of the reflection coefficient and the phase And the impedance on the Smith chart is obtained from these values. FIGS. 6 to 10 show the impedance measurement results obtained in this manner.

FIG. 6 shows the locus of impedance when a load that matches the impedance is connected when both the E-plane stub 4 _E and the H-plane stub 4 _H are at the stub reference position. In Figure 6, the E-plane stubs 4 _E between the stub reference position (E = 0) to the upper limit position (E = 39 mm), each position was fixed at 5mm intervals, each position of the fixed E surface stub 4 _E Each time the H plane stub 4 _H is moved from the stub reference position (H = 0) to the upper limit position (H = 39 mm), the impedance is plotted on a Smith chart. For example, the locus indicated as E = 0 in FIG.
The trajectory of impedance when the plane stub 4 _E is fixed at the stub reference position and the H plane stub 4 _H is moved.
The numbers shown along the trajectory indicates the position of H-plane stubs 4 _H. Naturally, the E-plane stub 4 _E and the H-plane stub 4 _H
When both are at the stub reference position, matching is achieved, so the starting point of the locus of E = 0 is at the origin (matching point) on the Smith chart. As the H-plane stub 4 _H moves away from the stub reference position, the impedance point deviates from the origin of the Smith chart. The locus of E = 0 has a diameter of 上 on the Smith chart and an absolute value (| Γ) of the reflection coefficient Γ.
|) Can be approximated by a circle in contact with one circle (a circle indicated by | Γ | = 1 in FIG. 6).

In FIG. 6, the E-plane stub 4 _E is
Looking at the trajectory when the H-plane stub 4 _H is moved while being fixed at the position of = 10, the position of the entire trajectory is changed as compared with the trajectory of E = 0, but similar to the case of E = 0 , The diameter is 1/2 on the Smith chart, and the absolute value of the reflection coefficient Γ (| Γ
|) Can be approximated by a circle tangent to the circle of “1”.
Similarly, when changing the fixing position of the E-plane stubs 4 _E, trace corresponding to the respective fixed positions, but its position changes, can be approximated in the same circle.

Here, a circular locus of impedance corresponding to each fixed position of the E-plane stub 4 _E shown in FIG.
The center of the circle locus) and the origin of the Smith chart (| Γ |
FIG. 11 shows an angle (hereinafter, referred to as a circle center angle) taken by a line connecting the center of a circle (= 1) with respect to a line having a reactance of “0” (x = 0) in a Smith chart.
become that way. The vertical axis fixed position E surface stub 4 _E in FIG. 11, the horizontal axis represents the circle center angle corresponding to the fixed position E surface stub 4 _E, respectively show. The circle center angle is set positive in the counterclockwise direction and negative in the clockwise direction on the Smith chart. Relationship between the position and the circle center angle of the E-plane stubs 4 _E can be approximated by the tangent (tan) curve of a trigonometric function.

This approximation function can be expressed by the following equation (1). E (θ ₁ ) = A ₁ + B ₁ tan {C ₁ (θ ₁ −D ₁ ) × 360 / 2π} (1) The left side E (θ ₁ ) of the equation ( ₁ ) is the position of the E plane stub 4 _E , θ ₁
Is the circle center angle of the circular locus. A ₁ , B ₁ ,
C ₁ and D ₁ are constants determined by the characteristics of the microwave circuit.

FIG. 6 shows a case where impedance matching is achieved when both the E-plane stub 4 _E and the H-plane stub 4 _H are at the stub reference position. Furthermore, the present inventors similarly measured the locus of impedance in a general case where impedance matching was not achieved when each of the stubs 4 _E and 4 _H was at the stub reference position. The results are shown in FIGS. In Figure 6, a point on the Smith chart of impedance when each stub 4 _E, 4 _H is in the reference position (hereinafter, referred to as initial impedance point) was on origin on the Smith chart. However, FIG.
9 to FIG. 9, the initial impedance point S in each figure is located at a position deviated from the origin on the Smith chart. Also, circular locus of impedance corresponding to each position of the E-plane stubs 4 _E is the absolute value of the reflection coefficient is the approximately adjacent to the circle "1", the diameter is larger than 1/2.

As a result of studying the above measurement results, the present inventors have found a remarkable fact. First, in the case of FIGS. 7 to 9 where impedance matching is not achieved when each of the stubs 4 _E and 4 _H is at the stub reference position,
When examining the relationship between each position of the E-plane stub 4 _E and the circle center angle of the corresponding circular locus of impedance, the relationship is determined when the stubs 4 _E and 4 _H are at the stub reference position. This is a fact that the result is substantially the same as the relationship in FIG. 11 in which impedance matching is achieved.

Second, looking at the circular locus group of impedance shown in FIGS. 7 to 9, the circular locus group shown in FIG. It has a common intersection G. Similarly, the circle trajectory groups shown in FIGS. 8 and 9 have approximately common intersection points G that meet in the area surrounded by a circle in each figure. Furthermore, it should be noted that these intersections G
Is a straight line passing through the origin on the Smith chart (in the examples of FIGS. 7 to 9, the line whose reactance is “0” (x = 0))
This is the fact that it is located at a line symmetrical position with respect to. This axis of symmetry does not necessarily correspond to the line with a reactance of “0” on the Smith chart, and the angle changes depending on the position of the waveguide on which the antenna is mounted. Regardless of impedance matching or mismatch, they appear at the same position on the Smith chart. Incidentally, in the case of FIG. 6 in which the matching is obtained, the initial impedance point S and the common intersection G of the circle locus group are both on the origin of the Smith chart.

[0021] The present inventors have that the first and second fact is similarly true also for the locus of impedance when moving the H-plane stubs 4 _H position fixed and E-plane stubs 4 _E of confirmed. FIG. 10 shows E-plane stubs 4 _E and H
From a state where the surface stub 4 _H not is consistent when it is in both stub reference position, securing the H-plane stubs 4 _H at each position, obtained by moving the E-plane stubs 4 _E in respective fixed positions 3 shows a locus of impedance. FIG.
To show the position of H-plane stubs 4 _H, the relationship between the circle center angle of the circular locus of the impedance corresponding to the position. FIG.
The relationship of 2 can also be approximated by a tangent curve.

This approximation function can be expressed by the following equation (2). H (θ ₂ ) = A ₂ + B ₂ tan {C ₂ (θ ₂ −D ₂ ) × 360 / 2π} (2) The left side H (θ ₂ ) of the expression ( ₂ ) is the position of the H plane stub 4 _H , θ ₂
Is the circle center angle of the circular locus. A ₂ , B ₂ ,
C ₂ and D ₂ are constants determined by the characteristics of the microwave circuit.

Each of the stubs 4 _E and 4 shown in FIGS.
Relationship between the positions of _H, and the circle center angle of the circular trajectory groups impedance also the stub 4 _E, 4 _H is not necessarily is consistent when in the stub a reference position, i.e. for any load, established This is as described above. further,
The present inventors have confirmed that when the mounting position of the antenna is changed, the characteristic curves that can be approximated by the tangent curves in FIGS. 11 and 12 shift in the horizontal axis direction, but the shape of the characteristic curves is maintained as it is. did.

[0024] Based on the above findings, the present inventors, when tuning the microwave circuit arbitrary load is connected, when the E-plane stubs 4 _E and H-plane stubs 4 _H are both stub reference position If you know the impedance,
Even if the impedance of each position of each stub 4 _E , 4 _H is not measured, each stub 4 _E , 4
We arrived at that the proper position of _H can be derived.

As is well known, if the absolute value of the reflection coefficient and its phase are measured at an arbitrary position in the waveguide of the microwave circuit, the impedance at that point is determined. That is,
The absolute value of the reflection coefficient at a certain position and its phase are equivalent to the impedance at that position. Therefore, in the present invention, knowing the initial impedance point of the Smith chart when the stubs 4 _E and 4 _H are at the stub reference position is synonymous with knowing the absolute value of the reflection coefficient and the phase at that position. Note that

[0026] Principle of the invention of claim 1 Hereinafter, the stub 4 _E, 4 _H by using the impedance when in the stub a reference position, the stub 4 _E whose impedance matching,
The principle of the method for deriving the proper position of 4 _H will be described.

For the microwave circuit to be tuned, it is assumed that the impedance (therefore, the absolute value of the reflection coefficient and its phase) when both the E-plane stub 4 _E and the H-plane stub 4 _H are at the stub reference position is known. . FIG. 13 shows a plot of the initial impedance point S on the Smith chart. In addition, when the microwave circuit is in a certain load state, the symmetry axis X on the above-mentioned Smith chart is obtained in advance. As described above, even if the impedance on the load side changes, the position of the symmetry axis X does not change. Then, the common intersection G of the above-described circle locus group of impedance is located at a position symmetrical with the initial impedance point S with respect to the symmetry axis X.
Is obtained (see FIG. 13).

[0028] than the above findings, the stub 4 _E, 4 impedance point on the Smith chart corresponding to the proper position _H where impedance matching (i.e., matching point) circular locus of impedance is present, of course the matching Passing through a point (origin of the Smith chart) O and passing through the common intersection G, the absolute value of the reflection coefficient on the Smith chart |
Γ | is a circle that touches the circle of “1”. There are two such circular trajectories as shown by reference numerals C1 and C2 in FIG. Either a circular locus of the two circular locus C1, C2, if a circular locus when you move the H-plane stubs 4 _H secure the E-plane stubs 4 _E, the other circular path, H by fixing the surface stub 4 _H corresponds to circular locus when you move the E-plane stubs 4 _E. That is, there are two sets of appropriate positions of the stubs 4 _E and 4 _H where the impedance matches. One of the positions (E) of the stubs 4 _E and 4 _H obtained from the circular locus C1
₁ , H ₁ ) and the other is the position (E ₂ , H ₂ ) of each stub 4 _E , 4 _H obtained from the circular locus C ₂ . Impedance matching can be achieved regardless of whether each of the stubs 4 _E and 4 _H is set at (E ₁ , H ₁ ) or (E ₂ , H ₂ ).

More specifically, each stub 4
Appropriate positions (E ₁ , H ₁ ) and (E ₂ , H ₂ ) of _E and 4 _H can be obtained. Please refer to FIG. Now, it is assumed that the absolute value of the reflection coefficient measured when both the E-plane stub 4 _E and the H-plane stub 4 _H are at the stub reference position is | Γ _S |, and the phase thereof is θ _S. The initial impedance point S at this time is represented by polar coordinates (| Γ _S |, θ on the Smith chart.
_S ). For simplicity, the symmetry axis X described above is
The length of the waveguide of the microwave circuit is set so that the reactance on the Smith chart matches the line of “0” (x = 0). Then, the polar coordinates of the intersection G are (|
Γ _S |, −θ _S ).

The circular trajectories C1 and C2 described with reference to FIG.
Is in contact with the circle of | Γ | = 1 and passes through the origin O of the Smith chart, so that these circular trajectories C1 and C2 have a radius of 1
/ 2 circles, and the center points of these circles exist on a circle having a radius of 1/2 centered on the origin of the Smith chart (indicated by a chain line in FIG. 14). From the theorem of geometry, the line connecting the intersections of the two circles (line OG in FIG. 14) is orthogonal to the line connecting the centers of the two circles (line O ₁ O _{2 in} FIG. 14), It is bisected by this line segment. Assuming that the middle point of the line segment OG is N, the following relationship is established. ∠O ₁ ON = ∠O ₂ ON = ψ cos ψ = (| Γ _S ／/ ₂ ) / (１ ／) = | Γ _S ψ ψ = cos ^-1 ΓΓ _S ｜

Therefore, assuming that the angle between the center O ₁ of the circular locus C1 and the symmetry axis X is θ ₁ and the angle between the center O ₂ of the circular locus C2 and the symmetry axis X is θ ₂ , these angles θ ₁ and θ 2 _Two
Can be obtained by the following equations (3) and (4). θ ₁ = -θ _S + ψ = -θ _S + cos ^-1 | Γ _S | ... (3) θ ₂ = -θ _S -ψ = -θ _S -cos ^-1 | Γ _S | ... (4)

The circle center angles θ ₁ and θ _{2 of the} circular trajectories C1 and C2
, The stubs 4 _E and 4 _E shown in FIGS.
By referring to the relationship between the position of _H and the circle center angle,
The positions of the stubs 4 _E and 4 _H corresponding to the angles θ 1 and θ ₂ can be known. For example, when the circle center angle θ ₁ is applied to the relationship shown in FIG. 11, the proper position E of the E-plane stub 4 _E is obtained.
_{When 1} is obtained and the circle center angle θ ₂ is applied to the relationship shown in FIG. 12, an appropriate position H ₁ of the H-plane stub 4 _H is obtained. Conversely, the angle θ ₂ may be applied to the relationship shown in FIG. 11 and the angle θ ₁ may be applied to the relationship shown in FIG. 12. In this case, another appropriate position (E ₂ , H ₂ ) is obtained as described above. is there.

[Structure and operation of the invention of claim 1] The invention of claim 1 is based on the above-mentioned principle, and the structure is as follows. That is, according to the first aspect of the present invention, a branch pipe branched from two orthogonal wall surfaces of the waveguide is provided in the middle of the rectangular waveguide connecting the microwave generator and the load. In an automatic tuning method of a microwave circuit, an E-plane stub is slidably inserted into an E-plane stub, and an H-plane stub is slidably inserted into the other branch pipe, and the position of each stub is adjusted to achieve impedance matching. 1) a step of measuring the absolute value of the reflection coefficient and the phase thereof when both the E-plane stub and the H-plane stub are at a position flush with the inner surface of the rectangular waveguide (hereinafter referred to as a stub reference position); (2) a step of obtaining each position of the E-plane stub and the H-plane stub whose impedance matches based on the absolute value of the reflection coefficient measured in the step (1) and its phase; and (3) the step (2). Asked for Moving the E-plane stub and the H-plane stub to each of the positions to achieve impedance matching between the microwave generator and the load. The step (2) is substantially the following (a) to ( g), ie, (a) fixing the E-plane stub at various positions and moving the H-plane stub to the entire movable range for each position of the fixed E-plane stub, In the circular locus of impedance on the Smith chart at each position (hereinafter referred to as a circular locus), the angle of a line segment connecting each position of the E-plane stub with the center of each circular locus and the origin on the Smith chart (Hereinafter referred to as a circle center angle) in advance, the H-plane stub is similarly fixed at various positions, and the E-plane stub is moved over the entire movable range for each position of the fixed H-plane stub. By moving Te, each position of the H-plane stubs and a process of previously obtained correspondence relationship between the circle center angle at that time, (b) E plane stub obtained by the step (a) or H
For at least one circular trajectory group of the surface stub,
Points on the Smith chart corresponding to the impedance when both the plane stub and the H plane stub are at the stub reference position;
A step of obtaining in advance a symmetry axis on the Smith chart where the common intersection point of the circle locus group is line-symmetric, and (c) a Smith determined by the absolute value of the reflection coefficient measured in the step (1) and its phase. Using a point on the chart (hereinafter referred to as an initial impedance point) and a symmetry axis obtained in the step (b), a point on the Smith chart that is line-symmetric with the initial impedance point with the symmetry axis interposed therebetween ( (Hereinafter referred to as a line symmetry point) and (d) passing through the line symmetry point and the matching point which is the origin on the Smith chart, and the absolute value of the reflection coefficient is “1” on the Smith chart. (E) obtaining the angles of the line segments connecting the centers of the two circles and the origin on the Smith chart; and (f) obtaining the angles of the lines connecting the centers of the two circles. E-plane stub position and circle found A step of determining the position of the E-plane stub corresponding to the angle of one of the line segments determined in step (e) with reference to the relationship with the angle; and (g) determining the position of the H-plane stub determined in step (a). Referring to the relationship between the position and the center angle of the circle to determine the position of the H-plane stub corresponding to the angle of the other line segment determined in step (e).

According to the first aspect of the present invention, in the step (1), for the microwave circuit to be automatically tuned, both the E-plane stub and the H-plane stub are set at the stub reference position, and the reflection at that time is set. Measure the absolute value of the coefficient and its phase. Then, in the next process (2),
Based on the absolute value and the phase of the reflection coefficient measured in the process (1), the appropriate positions of the E-plane stub and the H-plane stub whose impedance matches are obtained. The algorithm of the process executed in step (2) is represented by steps (a) to (g). The process in the step (2) may be any one in which the steps (a) to (g) are substantially executed. If the symmetry axis shown in the step (b) is known in advance, the angle (circle center angle) obtained in the steps (c) to (e) connecting the center of the two circles and the origin on the Smith chart ) Is uniquely determined geometrically, and thus the center angles of these circles can be directly obtained by arithmetic processing. If one of the two obtained circle center angles is applied to the relationship between the position of the E-plane stub and the circle center angle obtained in step (a), an appropriate position of the E-plane stub is obtained. If the other circle center angle is applied to the relationship between the H plane stub and the circle center angle, an appropriate position of the H plane stub is obtained. When the proper position of each stub is determined, in step (3), the E-plane stub and the H-plane stub 4 are moved to the respective determined positions to achieve impedance matching.

According to the first aspect of the present invention, when automatically tuning a microwave circuit to which an arbitrary load is connected, the E-plane stub and the H-plane stub are initially set at appropriate positions where impedance matching can be achieved. Note that this is a setting method. After initializing each stub to an appropriate position using the method of the present invention, the position of each stub is fine-tuned using a conventionally known feedback control or the like so that the absolute value of the reflection coefficient is minimized. I just need.

[Principle of Claim 2] The relationship between the E-plane stub and the center angle of the circle shown in FIG. 11 and the relationship between the H-plane stub and the center angle of the circle shown in FIG. , (2)
As described above, the approximation can be made by the tangent function shown in the equation.
The center angles of the two circles obtained in steps (c) to (e) are obtained by measuring the absolute value of the reflection coefficient and the phase when the E-plane stub and the H-plane stub are at the stub reference position. As described above, the proper position of each stub can be obtained by applying these circle center angles to the relationships shown in FIGS. 11 and 12, which are uniquely determined by the above equations (3) and (4). Therefore, a function can be set in advance by substituting the values of the circle center angles θ ₁ and θ ₂ obtained by the equations (3) and (4) into the tangent functions expressed by the equations (1) and (2). The appropriate position of each stub can be obtained simply by giving the absolute value and the phase of the reflection coefficient when the E-plane stub and the H-plane stub are at the stub reference position to the function.

That is, one appropriate position (E
₁ , H ₁ ) can be obtained by a function represented by the following equations (5) and (6). _{E 1 = A 1 + B 1} tan {C 1 (-θ S -360 ° + cos -1 | Γ S | + D 1) × 360 / 2π} ...... (5) H 1 = A 2 + B 2 tan {C 2 ( −θ _S −360 ° −cos ⁻¹ | { _S | + D ₂ ) × 360 / 2π} (6)

Further, another appropriate position (E
₂ , H ₂ ) can be obtained by a function represented by the following equations (7) and (8). _{E 2 = A 1 + B 1} tan {C 1 (-θ S -360 ° -cos -1 | Γ S | + D 1) × 360 / 2π} ...... (7) H 2 = A 2 + B 2 tan {(C _{2 (-θ S -360 ° + cos} -1 | Γ S | + D 2) × 360 / 2π} ...... (8)

The proper position (E) obtained by the above equations (5) and (6)
₁, H₁) Or the appropriate position obtained by equations (7) and (8)
(E_Two, H_Two) Set each stub in either position
Also, impedance matching can be achieved. In addition, above
In the above (5) to (8), θ₁, Θ_TwoAnd θ_SAngle direction
In order to make the values of “−θ” in equations (3) and (4)_STo [-θ
_S-360 °].

[Structure and Operation of the Invention of Claim 2] The invention of claim 2 is based on the above-described principle, and the structure is as follows. That is, according to a second aspect of the present invention, in the method according to the first aspect, the processing in the step (2) is performed by: And two functions obtained based on approximating the relationship between the position of the H-plane stub and the center of the circle, ie, the absolute value of the reflection coefficient and the phase thereof when both stubs are at the stub reference value. A first function relating the position of the E-plane stub whose impedance matches, and a second function relating the absolute value and phase of the reflection coefficient and the position of the H-plane stub whose impedance matches. By giving the absolute value of the reflection coefficient measured in the step (1) and the phase thereof to the function, the steps (a) to (g) are substantially executed, and the E-plane star whose impedance is matched is obtained. And characterized in that to determine the respective positions of the H-plane stubs.

According to the second aspect of the present invention, if the first function and the second function are determined in advance, both the E-plane stub and the H-plane stub are used as stub reference values in these functions. The position of the E-plane stub and the position of the H-plane stub whose impedance matches can be obtained simply by giving the absolute value of the reflection coefficient and the phase thereof at the position.

[Principle of the invention of claim 3] When the length of the waveguide changes, the phase of the circular locus group of impedance is displaced,
As a result, the relationship between each stub and the circle center angle shown in FIGS. 11 and 12 shifts (phase is displaced), or the symmetry axis between the initial impedance point on the Smith chart and the common intersection of the circle locus group changes. Doing was explained earlier. Step (a) is performed for each microwave circuit having a different waveguide length.
And the step (b) may be performed to determine the axis of symmetry,
In particular, it is troublesome to measure the relationship between the position of each stub and the angle of the circle center in step (a) every time the length of the waveguide changes.
Therefore, the present inventors have determined the relationship between each stub and the center angle of a circle obtained for a microwave circuit using a waveguide of a reference length (hereinafter, referred to as a reference waveguide) and the axis of symmetry thereof. A method for easily obtaining the relationship between each stub and the center of the circle and the axis of symmetry of a microwave circuit having a waveguide having an arbitrary length different from the reference waveguide has been considered.
Hereinafter, the principle will be described with reference to FIG.

First, with respect to the microwave circuit having the reference waveguide, from the group of circular locus of impedance when the E-plane stub is moved while the E-plane stub is fixed at each position.
The reference circular locus C ₀ is appropriately determined, and the circle center angle θ
Measure _{E0 beforehand} . This circle center angle θ _E0 becomes equal to the phase when the absolute value of the reflection coefficient becomes substantially “1” when the E-plane stub is fixed at a predetermined position and the H-plane stub is moved. This is obtained by measuring θ _{E0 (} hereinafter referred to as E reference phase). Similarly, when the H plane stub is fixed at a predetermined position and the E plane stub is moved, the phase θ _{H0 at} which the absolute value of the reflection coefficient becomes substantially “1” (hereinafter referred to as H reference phase) is measured. Keep it. When tuning a microwave circuit having a waveguide of an arbitrary length, at the same position as when the E reference phase θ _E0 is measured,
When the E-plane stub of the microwave circuit is fixed and the H-plane stub is moved, the phase (hereinafter referred to as E actual phase) θ _E0 ′ when the absolute value of the reflection coefficient becomes substantially “1” is measured. (The circular locus at this time is indicated by reference symbol C ₀ ′ in FIG. 15).
Similarly, the phase when the absolute value of the reflection coefficient becomes substantially “1” when the H-plane stub of the microwave circuit is fixed at the same position as when the H reference phase is measured and the E-plane stub is moved. (Hereinafter referred to as H actual phase) θ _H0 ′ is obtained. This H
The actual phase θ _H0 ′ does not necessarily need to be obtained by measurement. H
Since the deviation (displacement amount) of the H actual phase with respect to the reference phase is substantially the same as the deviation of the E actual phase with respect to the E reference phase, the deviation of the E actual phase with respect to the E reference phase is determined by measuring the E actual phase. This is because the H actual phase can be known from the H reference phase. Conversely, if the H actual phase is measured,
The value of the E actual phase can be known without measuring the E actual phase.

The E actual phase measured as described above and E
The difference between the reference phases (θ _E0 ′ −θ _E0 ) is equal to the shift amount of the relationship between the position of the E-plane stub and the center angle of the circle caused by the change in the length of the waveguide. Therefore, the relationship between the position of the E-plane stub obtained for the microwave circuit having the reference waveguide and the angle of the center of the circle is calculated by the difference (θ _E0 ′ −θ _E0 ).
, The relationship between the position of the E-plane stub and the angle of the center of the circle can be obtained for a microwave circuit having a waveguide of an arbitrary length. Similarly, the relationship between the position of the H-plane stub and the circle center angle obtained for the microwave circuit having the reference waveguide is corrected by the difference between the H actual phase and the H reference phase (θ _H0 ′ −θ _H0 ). For example, a relationship between the position of the H-plane stub and the angle of the center of the circle can be obtained for a microwave circuit having a waveguide of an arbitrary length.

The same applies to the case where a symmetry axis (hereinafter, referred to as a real symmetry axis) on a Smith chart is obtained for a microwave circuit having a waveguide of an arbitrary length. First, for a microwave circuit using a reference waveguide, an E-plane stub or H
A symmetry axis on the Smith chart (hereinafter referred to as a reference symmetry axis) is obtained from a group of circular locus traces of impedance on the Smith chart obtained by fixing any one of the surface stubs and moving the other stub. This reference symmetry axis is indicated by the symbol X in FIG. How much the reference symmetric axis X is displaced with respect to the E reference phase or the H reference phase is determined in advance by a displacement angle Δθ. In the example of FIG.
For simplicity, a waveguide whose length is such that the symmetry axis X coincides with the line whose reactance is “0” (x = 0) on the Smith chart is used as the reference waveguide. Δθ coincides with the E reference phase (−θ _E0 ). This displacement angle Δθ is maintained even if the length of the waveguide changes.
Therefore, if the E actual phase θ ₀ ′ (or H actual phase) is measured for a microwave circuit having a waveguide of an arbitrary length, by shifting the angle from the phase θ ₀ ′ by the displacement phase Δθ, The real symmetry axis X 'of the microwave circuit can be obtained.

[Structure and Operation of the Invention of Claim 3] The invention of claim 3 is based on the above-described principle, and the structure is as follows. That is, according to a third aspect of the present invention, in the method according to the first or second aspect, the step (a) includes the following steps (a1) to (a3).
In other words, (a1) the relationship between the position of the E-plane stub and the angle of the circle center for a microwave circuit having a rectangular waveguide having a reference length (hereinafter referred to as a reference waveguide); And the relationship between the position of the H plane stub and the circle center angle is measured in advance, and the circle center angle of the circular locus when the E plane stub is fixed at a predetermined position and the H plane stub is moved (hereinafter referred to as E reference). (A phase)) and a step of previously obtaining a center angle of a circular locus (hereinafter, referred to as an H reference phase) when the E-plane stub is moved while the H-plane stub is fixed at a predetermined position; In performing automatic tuning of a microwave circuit provided with a rectangular waveguide having an arbitrary length different from the reference waveguide, the E-plane stub of the microwave circuit is used to determine the E reference phase. Fix to the same position as the E-side stub and H-side When moving the tab, the absolute value is substantially "1" to become a point of the phase of the reflection coefficient (hereinafter, E referred actual phase) and the H-plane stubs in the microwave circuit, the H
When the E-plane stub is moved while being fixed at the same position as the H-plane stub when the reference phase was obtained, the phase at the point where the absolute value of the reflection coefficient becomes substantially “1” (hereinafter referred to as “H actual phase”) To
(A3) The relationship between the E-plane stub and the circle center angle obtained for the microwave circuit provided with the reference waveguide is obtained by measuring at least one of the actual phases. By correcting by an angle corresponding to the difference from the E reference phase, the relationship between the E-plane stub of the microwave circuit having the rectangular waveguide having the arbitrary length and the center angle of the circle is obtained. By correcting the relationship between the H-plane stub and the circle center angle obtained for the microwave circuit having the waveguide by an angle corresponding to the difference between the H actual phase and the H reference phase, the arbitrary length is obtained. Determining the relationship between the H-plane stub of the microwave circuit having the rectangular waveguide and the angle of the center of the circle, wherein said step (b) is the following step (b1) or (b2): , (B
1) Regarding the microwave circuit provided with the reference waveguide,
With respect to at least one of the E reference phase and the H reference phase, a displacement angle of a symmetry axis (hereinafter, referred to as a reference symmetry axis) on a Smith chart of a microwave circuit having the reference waveguide is obtained in advance. And (b)
2) When performing automatic tuning of the microwave circuit having the rectangular waveguide having an arbitrary length, the displacement angle of the reference symmetry axis is subtracted from the actual phase corresponding to the reference phase when the displacement angle is obtained. Determining the actual axis of symmetry (hereinafter, referred to as the actual axis of symmetry) on the Smith chart of the microwave circuit.
In step (b2), a line symmetry point is obtained by using the real axis of symmetry obtained in step (b2). In step (f), E is corrected in step (a3).
The position of the E-plane stub is determined using the relationship between the surface stub and the circle center angle, and in step (g), H is determined using the relationship between the H-plane stub and the circle center angle similarly corrected in step (a3). It is characterized in that the position of the plane stub is obtained.

According to the third aspect of the present invention, in the microwave circuit having the reference waveguide, in the step (a1),
The relationship between the position of the E-plane stub and the circle center angle and the relationship between the position of the H-plane stub and the circle center angle are measured, and the E reference phase and the H reference phase are obtained.
If the displacement angle of the reference symmetry axis is determined, the position of each stub and the center of the circle are tuned each time when tuning a microwave circuit having a waveguide of an arbitrary length different from the reference waveguide. There is no need to measure the relationship with the angle and determine the axis of symmetry of the microwave circuit. That is, for a microwave circuit having a waveguide of an arbitrary length, if the E real phase and the H real phase are measured in step (a2), these stubs of the microwave circuit are used using these real phases. And the symmetry axis (actual symmetry axis) on the Smith chart can be easily obtained.

[Principle of Claim 4] After the E-plane stub and the H-plane stub are initially set at appropriate positions for impedance matching, the normal value of the reflection coefficient | Γ | is minimized as much as possible. By feedback control etc.
The position of each stub is finely adjusted. At this time, if the load suddenly fluctuates due to external influences, the appropriate position of each stub that matches the impedance also suddenly fluctuates greatly. Disappears. As a result, it is necessary to reset each stub. Therefore, it is complicated to execute the above-described process (1) of moving each stub to the stub reference position and obtaining the absolute value of the reflection coefficient and the phase at that position. Therefore, the present inventors measure the absolute value and the phase of the reflection coefficient when each stub is at the stub reference position when re-determining the appropriate position of each stub for such a sudden load change. A method that can quickly determine the appropriate position of each stub without doing so was considered. Hereinafter, the principle will be described.

When the load fluctuates rapidly, the E-plane stub and
And position E of H-plane stub₁, H₁Figure 1
1, the relationship between the position of each stub shown in FIG.
From the staff, the position E of each stub₁, H₁Impey corresponding to
Circle center angle θ of the circle of dance _E, Θ_HCan ask for
it can. Note that the microwave frequency to be tuned
If the length of the waveguide in the path is different from the reference waveguide,
The corrected stub positions described in the invention of item 3 and
Circle corresponding to each stub position using the relationship of circle center angle
The center angle can be determined. Also, the load changes suddenly.
The absolute value of the reflection coefficient | Γ |
We can know by measuring. Stub position E₁,
H₁The circular locus of each impedance corresponding to
Contact the circle with | Γ | = 1 on the Smith chart and load
Point expressed by absolute value | Γ | of reflection coefficient at sudden change and phase θ
, These two circular trajectories C_E1, C
_H1Is uniquely determined. This is shown in FIG.

The two determined circular trajectories C _E1 and C _H1 have another intersection G in addition to the point F represented by the absolute value | Γ | This intersection G
Are common intersections through which a group of circular locus of impedance corresponding to each position of the E-plane stub (or the H-plane stub) passes. Therefore, a point that is symmetric with respect to the axis of symmetry (or the actual axis of symmetry) X on the Smith chart of the microwave circuit, which is obtained at the time of the initial initialization of each stub, indicates that each stub is the stub reference position. Is the impedance point (initial impedance point) S at the point of If the initial impedance point S is known, the position of each stub whose impedance matches can be obtained by performing the above-described process (2).

[Structure and Operation of the Invention of Claim 4] The invention described in claim 4 is based on the above-described principle, and the structure is as follows. That is, the invention according to claim 4 provides the method according to any one of claims 1 to 3, further comprising the following steps (4) to (7), ie, (4) the steps (1) to ( After the positions of the E-plane stub and the H-plane stub are initialized according to 3), while the microwave circuit is operating while controlling the positions of both stubs in a direction in which the absolute value of the reflection coefficient becomes smaller, the reflection is performed. (5) monitoring the sudden change in the absolute value of the coefficient; and (5) detecting the sudden change in the absolute value of the reflection coefficient in the step (4). And (6) measuring E based on the absolute value of the measured reflection coefficient and its phase.
A process of newly calculating the absolute value and the phase of the reflection coefficient when both the plane stub and the H-plane stub are at the stub reference position; and (7) calculating the absolute value and the phase of the reflection coefficient obtained in the step (6). Moving the E-plane stub and the H-plane stub to a position where impedance matching can be achieved by performing the above-mentioned steps (2) to (3) using the step (3). Steps (h) to (j), that is, (h) the relationship between the position of the E-plane stub and the center angle of the circle obtained in step (a), and
By referring to the relationship between the position of the plane stub and the circle center angle, the circle center angle corresponding to the position of the E plane stub and the circle corresponding to the position of the H plane stub when the reflection coefficient fluctuates rapidly And (i) a circle center angle corresponding to the position of the E-plane stub obtained in step (h), and the absolute value of the reflection coefficient on the Smith chart is “1”. Touching the circle and the process (5)
Has a first circle passing through a point on the Smith chart corresponding to the absolute value of the reflection coefficient and the phase thereof measured in the above, and a circle center angle corresponding to the position of the H-plane stub similarly obtained in the step (h). And a point on the Smith chart that passes through a point on the Smith chart corresponding to the absolute value of the reflection coefficient measured in the step (5) and the phase thereof while being in contact with the circle whose absolute value of the reflection coefficient is “1”. The process of finding the circle of 2,
(J) Of the two intersections of the first and second circles, the other intersection different from the one intersection on the Smith chart corresponding to the absolute value of the reflection coefficient measured in step (5) and its phase In contrast, an impedance point on the Smith chart that is line-symmetric with respect to the symmetry axis obtained in the step (b) is obtained, and from this impedance point, when both the E-plane stub and the H-plane stub are at the stub reference position. And a process of newly obtaining the absolute value of the reflection coefficient and the phase thereof.

According to the present invention, the absolute value and the phase of the reflection coefficient when the load fluctuates rapidly are measured, and the position of each stub at that time is known, so that each stub is obtained. Since the absolute value of the reflection coefficient and its phase when the stub is at the stub reference position can be obtained, each time the load fluctuates suddenly, each stub is returned to the stub reference position, and the absolute value of the reflection coefficient and its phase are returned. Is not required to be measured, and each stub can be quickly moved to an appropriate position where the impedance is matched.

[Principle of the Invention of Claim 5] The initial impedance point S described in the principle of the invention of claim 4 can also be obtained by calculation. Hereinafter, description will be made with reference to FIG. The circle center angle θ _E of the circle locus C _E1 can be expressed by the following equation (9) using a tangent function that approximates the relationship between the E-plane stub and the circle center angle shown in FIG.

[0054]

(Equation 1)

Similarly, the circle center angle θ _H of the circular locus C _H1 is
The following equation (10) can be used using a tangent function approximated to the relationship between the H-plane stub and the circle center angle shown in FIG.

[0056]

(Equation 2)

In the equation (9), E is the position of the E-plane stub,
A ₁ , B ₁ , C ₁ , and D ₁ are constants. In the equation (10), H is the position of the H-plane stub, and A ₂ , B ₂ , C ₂ , and D ₂ are constants.

The coordinates of the point F represented by the polar coordinates (| Γ |, θ) are transformed into the rectangular coordinates (a,
Rewriting in b), F (a, b) = (| Γ | cos θ, | Γ | sin θ).

Here, _{assuming that} the radius of the circular locus C _E1 is r _E , the coordinates of the center point O _E are ((1-r _E ) cos θ _E , (1-r _E ) sin θ _E ). . Similarly, when the radius of the circular path C _H1 and r _H, the coordinates of the center point O _H becomes _{((1-r H) cos} θ H, (1-r H) sin θ H).

Therefore, the circular locus C _E1 is represented by the following equation. ｛X- (1-r _E ) cos θ _E ｝ ² + ｛y- (1-r _E )
sin θ _E ｝ ² = r ^{2 The} above equation can be rewritten as follows. x ² -2x (1-r _E ) cos θ _E + y ² -2y (1-r _E ) sin θ _E + 1-2r _E = 0 (11)

Similarly, the circular locus C _H1 is expressed by the following equation. _{^{x 2 -2x (1-r H}} ) cos θ H + y 2 -2y (1-r H) sin θ H + 1-2r H = 0 ...... (12)

Since both the circular trajectories C _E1 and C _H1 pass through the point F (a, b), the following relation is obtained from the equation (11). _{^{a 2 -2a (1-r E}} ) cos θ E + b 2 -2b (1-r
_E ) sin θ _E + 1-2r _E = 0 From the above equation, the radius r _E of the circular locus C _E1 is represented by the following equation (13).

[0063]

(Equation 3)

Similarly, from equation (12), the radius r of the circular locus C _H1
H is expressed by the following equation (14).

[0065]

(Equation 4)

[0066] Here, the center O _E of the circular path C _E1, the slope m of the straight line L ₁ passing through the center O _H of circular path C _H1 represented by the following formula (15).

[0067]

(Equation 5)

If the inclination of the straight line L ₂ passing through the points F and G is m ′, the two straight lines L ₁ and L ₂ are orthogonal to each other.
The following relationship holds: m · m ′ = − 1 Therefore, m ′ = − 1 / m (16) The slope m 'is given by the following equation (17). m ′ = (y′−b) / (x′−a) (17) From the equations (16) and (17), the following equation (18) is obtained. x ′ + m · y ′ = a + m · b (18)

A straight line L ₁ passing through the points O _E and O _H is given by the following equation (19)
It is represented by y− (1−r _H ) sin θ _H = m ｛x− (1−r _H ) cos θ _H ｝ (19) This straight line L ₁ is the intersection of the line segment FG ((x ′ + a) / 2 ,
(Y '+ b) / 2), the following equation (2) is obtained from the equation (19).
0) is obtained. (Y ′ + b) / 2− (1−r _H ) sin θ _H = m ｛(x ′ + a) / 2− (1−r _H ) cos θ _H ｝ (20) The following equation (21) is obtained. −mx ′ + y ′ = 2 (1−r _H ) sin θ _H −b + ma−2 m (1−r _H ) cos θ _H (21)

From equations (18) and (21), the intersection G (x ′,
y ′) is expressed by the following equations (22) and (23).

[0071]

(Equation 6)

In the above equations (22) and (23), F (a, b) = (|
By substituting the values of Γ | cos θ and | Γ | sin θ), the following equations (24) and (25) are obtained.

[0073]

(Equation 7)

The point G obtained by the above equations (24) and (25)
(X ′, y ′) is a common point through which the circular locus group of impedance passes regardless of the positions E and H of the stubs. Here, if the length of the waveguide of the microwave circuit is set such that the reactance on the Smith chart coincides with the line of “0” (x = 0) on the Smith chart, the symmetry axis X S (x ′, − y ′) which is line-symmetric with respect to point G with respect to
Is the initial impedance point when each stub is at the stub reference position. The absolute value | Γ | ′ of the reflection coefficient corresponding to the initial impedance point S and its phase θ ′ are represented by the following equations (29) and (30).

[0075]

(Equation 8)

By executing the process (2) using the absolute value | Γ | ′ of the reflection coefficient obtained by the above equations (29) and (30) and its phase θ ′, the stub of each impedance matching stub can be obtained. The position can be determined.

[Structure and Operation of the Invention of Claim 5] The invention described in claim 5 is based on the above-described principle, and the structure is as follows. That is, according to a fifth aspect of the present invention, in the method according to the fourth aspect, the process in the step (6) includes the step of: determining a relationship between the position of the E-plane stub obtained in the step (a) and a circle center angle; The absolute value and phase of the reflection coefficient when the absolute value of the reflection coefficient fluctuates rapidly, and the E-plane stub and the H-plane stub are both stubs, based on the relationship between the position of the H-plane stub and the center angle of the circle. An approximation function relating the absolute value of the reflection coefficient and its phase at the reference position, the circle center angle corresponding to the position of the E-plane stub when the absolute value of the reflection coefficient fluctuates rapidly, By giving the center angle of the circle corresponding to the position of the H-plane stub, the absolute value of the reflection coefficient when the absolute value of the reflection coefficient fluctuates sharply, and the phase thereof, the processes (h) to (h) are substantially performed. j)
It is characterized in that the absolute value and the phase of the reflection coefficient when both the E-plane stub and the H-plane stub are at the stub reference position are obtained.

[0078] According to the invention described in claim 5, the circle center angle corresponding to the position of the E-plane stubs when the absolute value fluctuates rapidly reflection coefficient, also corresponding to the position of H-plane stubs 4 _H By giving the circle center angle, the absolute value of the reflection coefficient at that time and its phase to the approximation function, the absolute value of the reflection coefficient when each stub is at the stub reference position and its phase can be calculated. Each stub can be quickly moved to an appropriate position where the impedance matches.

[0079]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a schematic configuration of an embodiment of a microwave circuit using the method of the present invention.
Here, a plasma dry etching apparatus for an integrated circuit (IC) using microwaves will be described as an example.

In the figure, reference numeral 11 denotes a microwave power supply.
The power from the microwave power supply 11 is supplied to the microwave generator 12
Given to. The microwave power generated by the microwave generator 12 propagates through the rectangular waveguide 1 having a rectangular cross section, and is supplied to a plasma generation chamber (hereinafter referred to as a load) 13 which is a load. An isolator 14 and a directional coupler 1 are provided between a microwave generator 12 and a load 13.
5. The stub matching devices 2 _E and 2 _H are interposed in that order. Between the stub matching device 2 _E, 2 _H and the load 13, the waveguide 1a for extension is interposed as necessary.

The directional coupler 15 separates an incident wave and a reflected wave. Each separated microwave is supplied to a power meter 16
And each power value is measured. The constant power control of the microwave power supply 11 is performed by the measured incident power.

The stub matching devices 2 _E and 2 _H are slidable in the branch tubes 3 _E and 3 _H branched from two orthogonal wall surfaces of the rectangular waveguide 1 as described with reference to FIGS. E inserted in
Comprising a surface stub 4 _E and H plane stub 4 _H. Each of the stubs 4 _E and 4 _H is driven to an arbitrary position by a screw feed mechanism (not shown) using a pulse motor. Stub matching device 2
Sensors (not shown) for detecting that the stubs 4 _E and 4 _H have reached positions (stub reference positions) that are flush with the inner surface of the rectangular waveguide 1 are provided at _E and 2 _H , respectively. ing.

In the rectangular waveguide 1 on the input side of the stub matching devices 2 _E and 2 _H , an antenna 19 composed of three (or five) probes is, for example, λ / 8 (λ is the wavelength of a microwave). Are arranged at intervals. The antenna 19 detects a voltage standing wave in the rectangular waveguide 1. The detection signal is sent to the controller 1
7 given. The controller 17 measures the absolute value and the phase of the reflection coefficient at the position where the antenna 19 is installed based on the detection signal, and performs initial setting and fine adjustment of the positions of the stubs 4 _E and 4 _H so as to achieve impedance matching. Make adjustments.

The operation of the above-described embodiment will now be described with reference to FIGS.
This will be described with reference to the flowchart shown in FIG. Here, a case where a microwave circuit having a waveguide of an arbitrary length is automatically tuned will be described as an example.

In step S1 (setup processing),
In tuning a microwave circuit having a waveguide of an arbitrary length, the following three data are measured in advance for a microwave circuit having a waveguide of a reference length. This step S1 corresponds to the process (a) of the invention described in claim 3.
1) and step (b1).

First, the relationship between the position of the E-plane stub 4 _E shown in FIG. 11 and the circle center angle and the relationship between the position of the H-plane stub 4 _H shown in FIG. 12 and the circle center angle are measured. . Then, the constants A ₁ ,
The values of B ₁ , C ₁ , D ₁ and A ₂ , B ₂ , C ₂ , D ₂ are determined.

Second, when the E-plane stub 4 _E is fixed at a predetermined position and the H-plane stub 4 _H is moved, the circle center angle (E reference phase) θ _E0 of the circular locus and the H-plane stub 4 _H are determined. A circle center angle (H reference phase) θ _H0 of the circular locus when the E-plane stub 4 _E is moved while being fixed at a predetermined position is measured. In this embodiment,
The center angle of the circle when the E-plane stub 4 _E is fixed at the stub reference position is E reference phase θ _E0, and similarly, the center angle of the circle when the H-plane stub 4 _H is fixed at the stub reference position is the H reference phase θ _H0. And

Third, the symmetry axis (reference symmetry axis) on the Smith chart of the microwave circuit having the reference waveguide with respect to at least one of the E reference phase θ _{E0 and the} H reference phase θ _H0. ) Is obtained in advance. In the present embodiment, the displacement angle Δθ _E of the reference symmetric axis with respect to the E reference phase θ _E0 is determined. In the present embodiment, the reference symmetry axis of the microwave circuit having the reference waveguide has a reactance “0” (x =
The displacement angle Δθ _E coincides with the E reference phase θ _E0 since the waveguide having a length that matches the line 0) is used as the reference waveguide. Here, Δθ _E = −θ _E0 in consideration of the angle direction.

Then, the equations (5) to (8) in which the respective constants are determined, the E reference phase θ _E0 and the H reference phase θ _H0, and the displacement angle Δθ _E are stored in the controller 17. . Thus, the setup process is completed. Hereinafter, automatic tuning proceeds under the control of the controller 17.

[0090] In step S2, the micro-wave circuit with an arbitrary length of the waveguide, to fix the E-plane stubs 4 _E in position, when you move the H-plane stubs 4 _H, absolute reflection coefficient Phase where the value | Γ | becomes approximately “1” (E actual phase)
Is measured. Here, when the E-plane stub 4 _E is fixed at the stub reference position and the H-plane stub 4 _H is moved in accordance with the condition in which the E reference phase θ _E0 is measured for the microwave circuit having the reference waveguide. The absolute value of the reflection coefficient | Γ |
Is substantially equal to “1”, and the E actual phase θ _E0 ′ is measured. Similarly,
When the H-plane stub 4 _H is fixed at the stub reference position and the E-plane stub 4 _E is moved, the phase (H actual phase) θ _H0 ′ at which the absolute value of the reflection coefficient | Γ | Ask. As described above, since the deviation (displacement amount) of the H actual phase with respect to the H reference phase is substantially the same as the deviation of the E actual phase with respect to the E reference phase, the H actual phase does not necessarily need to be obtained by measurement. In this embodiment, by measuring the E actual phase, E
Since the displacement amount of the E actual phase with respect to the reference phase is known, the H actual phase θ _H0 ′ is determined from the displacement amount and the H reference phase. This step S2 corresponds to the step (a2) of the present invention.

In step S3, the displacement angle Δθ _E (= −θ _E0 ) previously obtained in step S1 is subtracted from the E actual phase θ _E0 ′ measured in step S2.
The angle of the real symmetry axis is obtained for a microwave circuit having a waveguide of an arbitrary length. This step S3 is defined in claim 3
(See FIG. 15). Specifically, the angle θ _E ′ of the real symmetry axis is obtained by the following equation. θ _E ′ = θ _E0 ′ −Δθ _E = θ _E0 ′ + θ _{E0 The} controller 17 stores the angle θ _E ′ of the real axis of symmetry.

[0092] In step S4, the microwave circuit is a tuned object is set to both stub reference position E surface stub 4 _E and H plane stub 4 _H, the absolute value of the reflection coefficient of the time | gamma _S | a The phase θ _S is measured. This step S4 corresponds to the process (1) of the invention described in claim 1.

[0093] In step S5, 'by correcting with the phase theta _S relative to the real axis of symmetry' a phase theta _S measured in step S4 angle theta _E real symmetry axis determined in step S3 obtained. Specifically, the phase θ _S ′ is obtained by the following equation. θ _S '= θ _S -θ'

In step S6, the absolute value | Γ _S | of the reflection coefficient measured in step S4 and the phase θ _S ′ obtained in step S5 are substituted into the above-mentioned equations (5) to (8) to obtain Each stub 4 _E , 4 whose impedance matches
Position of _{H (E 1, H 1)} , determine the (E _2, H _2). Note that the corrected value of the phase θ _S ′ is given as the value of the phase θ _{S in} the equations (5) to (8). This step S5 corresponds to the second aspect of the present invention.

In step S7, the values obtained in step S6
Each stub 4_E, 4_HTwo appropriate positions (E₁,
H₁), (E_Two, H_Two), Select one of them
You. In this embodiment, each stub 4_E, 4_H3 movable range
Each stub 4_E, 4_HInitial position
About 20mm, which is almost in the middle,
Is preferred. Each stub 4_E, 4_HIntermediate initial position of
If it is set close to the position, it will be
Each stub 4 around the initial position_E, 4_HCan move positive and negative
This is because the range becomes wider. Therefore, this step S7
Then, E side stub 4 _EPosition E₁, E_TwoAnd E =
Select a pair with a value closer to 20 mm and move each pair to that position.
Tab 4_E, 4_HTo move. This step S7
This corresponds to step (3) of the invention described in item 1.

By the above processing, each of the stubs 4 _E and 4 _H
Is completed. The following steps are for each stub 4
_E, 4 _H after initializing the respective stub 4 _E, 4 process for maintaining a fine adjustment to the impedance of matching the positions of _H, and each stub 4 _E which load is executed when the sudden change, 4 is a resetting processing of _H.

In step S8, the absolute value of the reflection coefficient | Γ
Stub 4 so that | becomes as small as possible._E, 4_HPosition of
Fine-tune. Step S8 is well known in the art.
Auto tuning process is not detailed
However, each stub 4_E, 4_HIs fine-tuned
It is. Each stub 4 as above_E, 4_HIs initialized
By doing so, each stub 4_E, 4_HIs, for example, in FIG.
Position P of area A shown_AMove closer to. This area A
Within, the reflection coefficient simply decreases according to the position of the stub.
Or simply increase. This
In the area of a simple gradient such as
Tab 4_HAnd fix the other E-plane stub 4 _EFine movement (example
(For example, about 0.1 mm), the reflection coefficient becomes small.
Direction exists. E-plane stub 4 in that direction_ETweaked
The reflection coefficient gradually decreases, and
It grows bigger. That is, an inflection point appears. Inflection point
Is detected, the E-plane stub 4_E
Is fixed in that position, and the other H-plane stub 4_HAs well as fine
To find the direction in which the reflection coefficient decreases. Soshi
H-plane stub 4_HIs slightly moved. that's all
Is repeated until the reflection coefficient falls below the specified value.
When the reflection coefficient falls below a predetermined value,
Stub 4_E, 4_HIs fixed.

In step S9, the absolute value of the reflection coefficient | Γ
Is constantly monitored to see if it suddenly fluctuates. If there is no rapid fluctuation, the automatic tuning process in step S8 is continued. On the other hand, when the absolute value | Γ | of the reflection coefficient fluctuates rapidly, as described with reference to FIG. 17, the stubs 4 _E and 4 _H can no longer be moved to appropriate positions where impedance matching can be achieved in normal automatic tuning. Since it is not possible, the stubs 4 _E and 4 _H after step S10
Move on to the resetting process. This step S9 corresponds to the step (4) of the invention described in claim 4.

In step S10, the absolute value of the reflection coefficient |
The absolute value of the reflection coefficient | Γ | and the phase θ after the sudden change of 変 動 | are measured. This step S10 is defined in claim 4
Corresponds to the process (5) of the invention described in (1).

In step S11, the phase θ measured in step S10 is converted to the actual symmetry axis X ′ of the microwave circuit.
Is corrected to the phase based on. The corrected phase θ ″ is obtained by the following equation: θ ″ = (− 360 °) −θ _E ′ + θ In the above equation, θ is the measured phase, and θ _E ′ is the actual symmetry obtained in step S3. The angle of the axis. Here, in order to adjust the angle direction, (−36
0 °).

In step S12, the absolute value | Γ | of the reflection coefficient measured in step S10 and the correction phase θ ″ obtained in step S11 are described above in (24) through (30).
By providing the approximation function shown in equation, the stub 4 _E, 4 _H absolute value of the reflection coefficient when in the stub reference position | calculates | 'and the phase theta _S' the gamma _S. In addition,
The value of the above-mentioned correction phase θ ″ is given as the value of the phase θ in the equations (24) to (30). This step S12 corresponds to the fifth aspect of the present invention.

In the equations (24) to (30), the circle center angle θ _E corresponding to the position of the E-plane stub 4 _E when the absolute value of the reflection coefficient fluctuates rapidly is obtained as follows.
First, the relationship between the position and the circle center angle of the E-plane stubs obtained in step S1, determine the circle center angle giving the position of the E-plane stubs 4 _E when the absolute value of the reflection coefficient varies abruptly. Since this circle center angle corresponds to the case of the reference waveguide, in the case of a waveguide of an arbitrary length, the E actual phases θ _E0 ′ and E obtained in step S2 are further obtained from this circle center angle. The value obtained by subtracting the difference (θ _E0 ′ −θ _E0 ) from the reference phase θ _E0 is defined as the circle center angle θ _E.

Similarly, the circle center angle θ corresponding to the position of the H-plane stub when the absolute value of the reflection coefficient fluctuates rapidly
_H is obtained by giving the position of the H-plane stub 4 _H at the time when the absolute value of the reflection coefficient sharply changes to the relationship between the position of the H-plane stub obtained in step S1 and the circle center angle, and obtaining the circle center angle.
Further, from this circle center angle, the difference between the H actual phase θ _H0 ′ and the H reference phase θ _H0 obtained in step S2 (θ _H0 ′ −θ _H0 )
The value is referred to as the circle center angle θ _H minus.

By the above-described calculation processing in step S12,
And each stub 4_E, 4_HIs at the stub reference position
Absolute value of reflection coefficient ｜ Γ_S’| And its phase θ_S’
Returns to step S6, the absolute value of the reflection coefficient |
Γ_S’| And its phase θ_S′, Each stub 4_E,
4_HIs calculated and then selected in step S7.
Stub 4 in proper position_E, 4_HSet. Above
Each stub 4 _E, 4_HIs complete,
Thereafter, the process proceeds to the normal automatic tuning in step S8.
You.

The present invention is not limited to the above embodiment, but can be modified as follows. (1) In the above embodiment, the relationship between the position of each of the stubs 4 _E and 4 _H shown in FIGS. 11 and 12 and the circle center angle was approximated by a tangent function. By giving a circle center angle to this look-up table, each stub 4 _E ,
The position of 4 _H may be directly read.

(2) For a microwave circuit having a waveguide of an arbitrary length to be tuned, each stub 4
_E, 4 relationships and positions the circle center angle of _H, if to measure the symmetry axis on the Smith chart, as described in the above embodiment, the microwave circuit comprising a reference waveguide each It is not necessary to determine the relationship between the positions of the stubs 4 _E and 4 _H and the center angle of the circle.

[0107]

As apparent from the above description, the present invention has the following effects. According to the first aspect of the present invention, by measuring the absolute value and the phase of the reflection coefficient when the E-plane stub and the H-plane stub are both at the stub reference position, the appropriate position of each stub whose impedance matches is measured. Can be obtained, so that the initial setting of each stub can be quickly performed upon automatic tuning of the microwave circuit.

According to the second aspect of the present invention, the absolute value and the phase of the reflection coefficient when both the E-plane stub and the H-plane stub are at the stub reference position are determined by the first and second functions. , An appropriate position of each stub whose impedance matches can be easily obtained.

According to the third aspect of the present invention, if the relationship between the position of each stub and the angle of the center of the circle is measured for the microwave circuit having the reference waveguide, the waveguide having an arbitrary length can be measured. When tuning a microwave circuit with a tube, it is not necessary to measure the above relationship each time.
Initial setting of each stub can be performed more quickly.

According to the fourth aspect of the present invention, when the load fluctuates rapidly due to an external influence, the impedance matching and the phase are measured based on the measurement of the absolute value of the reflection coefficient and its phase at that time. The appropriate position of the stub can be determined. That is, since the appropriate position of each stub can be obtained without returning each stub to the stub reference position, it is possible to quickly reset each stub when the load changes abruptly.

According to the fifth aspect of the present invention, when the load suddenly fluctuates due to an external influence, the absolute value of the reflection coefficient at that time and its phase are given to the approximation function, so that each stub can be converted into a stub. The absolute value and the phase of the reflection coefficient at the reference position can be easily obtained.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of a microwave circuit using a method of the present invention.

FIG. 2 is an external perspective view of a stub matching device.

FIG. 3 is a sectional view of a stub matching device.

FIG. 4 is a flowchart illustrating a procedure of a tuning method according to the embodiment.

FIG. 5 is a flowchart illustrating a procedure of a tuning method according to the embodiment.

FIG. 6 is a diagram illustrating an example of a circular locus group of impedances when an E-plane stub is fixed and an H-plane stub is moved.

FIG. 7 is a diagram illustrating another example of a circular locus group of impedances when the E-plane stub is fixed and the H-plane stub is moved.

FIG. 8 is a diagram showing another example of a circular locus group of impedances when the E-plane stub is fixed and the H-plane stub is moved.

FIG. 9 is a diagram illustrating another example of a circular locus group of impedances when the E-plane stub is fixed and the H-plane stub is moved.

FIG. 10 is a diagram illustrating an example of a circular locus group of impedance when an H-plane stub is fixed and an E-plane stub is moved.

FIG. 11 is a graph showing the relationship between the position of an E-plane stub and the center angle of a circle.

FIG. 12 is a graph showing the relationship between the position of the H-plane stub and the angle of the center of the circle.

FIG. 13 is a diagram for explaining the principle of the present invention.

FIG. 14 is a diagram for explaining the principle of the present invention.

FIG. 15 is a diagram illustrating the principle of the present invention.

FIG. 16 is a diagram for explaining the principle of the present invention.

FIG. 17 is a graph for explaining a problem of the conventional example.

[Explanation of symbols]

1 ... rectangular waveguide 2 _E, 2 _H ... stub matching device 4 _E ... E surface stub 4 _H ... H surface stub 11 ... microwave power supply 12 ... microwave generator 13 ... load 14 ... isolator 15 ... directional coupler 16 Power meter 17 Controller 19 Antenna

Claims (5)

[Claims] 1. A branch pipe branching from two orthogonal wall surfaces of a microwave generator and a load is provided in the middle of a rectangular waveguide connecting the microwave generator and a load, and an E-plane stub is provided in one of the branch pipes. In an automatic tuning method of a microwave circuit in which an H-plane stub is slidably inserted into the other branch pipe and the position of each stub is adjusted to achieve impedance matching, (1) E-plane stub and Measuring the absolute value of the reflection coefficient and its phase when the H-plane stub is at a position flush with the inner surface of the rectangular waveguide (hereinafter referred to as a stub reference position); and (2) the step ( A process of obtaining the positions of the E-plane stub and the H-plane stub whose impedance matches based on the absolute value and the phase of the reflection coefficient measured in 1); and (3) each position obtained in the process (2). E side star Moving the stub and the H-plane stub to achieve impedance matching between the microwave generator and the load. The step (2) is substantially the following steps (a) to (g): (A) fixing the E-plane stub at various positions, and moving the H-plane stub to the entire movable range at each position of the fixed E-plane stub;
In a circular locus of impedance on the Smith chart at each position of the plane stub (hereinafter referred to as a circular locus), a line segment connecting each position of the E-plane stub with the center of each circular locus and the origin on the Smith chart. (Hereinafter referred to as circle center angle), the H-plane stub is similarly fixed at various positions, and the E-plane stub is movable at each position of the fixed H-plane stub. A step of previously determining the correspondence between each position of the H-plane stub and the angle of the circle center at that time by moving the entire area, and (b) an E-plane stub or an H-plane stub obtained in the step (a). For at least one circular locus group, a point on the Smith chart corresponding to the impedance when the E-plane stub and the H-plane stub are both at the stub reference position, and a common intersection point of the circular locus group are line-symmetric. (C) a point on the Smith chart determined by the absolute value of the reflection coefficient measured in the step (1) and its phase (hereinafter referred to as an initial impedance point). Using the symmetry axis determined in the step (b) to determine a point on the Smith chart (hereinafter, referred to as a line symmetry point) that is line-symmetric with the initial impedance point with respect to the symmetry axis; d) a process of obtaining two circles that pass through the line-symmetric point and the matching point that is the origin on the Smith chart, and that are in contact with a circle whose absolute value of the reflection coefficient is “1” on the Smith chart; (E) a process of calculating the angle of a line segment connecting the center of the two circles and the origin on the Smith chart; and (f) the position of the E-plane stub and the circle center angle obtained in the process (a). Referring to the relationship, the process (e) And (g) referring to the relationship between the position of the H-plane stub and the center angle of the circle determined in step (a) above. A step of obtaining the position of the H-plane stub corresponding to the angle of the other line segment obtained in the step (e). 2. The method according to claim 1, wherein in the step (2), the relationship between the position of the E-plane stub and the angle of the circle center determined in the step (a) and the position of the H-plane stub are set. And the circle center angle, the two functions obtained based on approximation, that is, the impedance and the absolute value of the reflection coefficient and the phase when both stubs are both at the stub reference value, and the impedance matches The first function relating the position of the E-plane stub, the absolute value of the reflection coefficient and its phase, and the H that matches the impedance
By giving the absolute value of the reflection coefficient measured in the step (1) and the phase thereof to a second function relating the position of the surface stub, the steps (a) to (g) are substantially performed. And determining the respective positions of the E-plane stub and the H-plane stub whose impedance is matched. 3. The method according to claim 1, wherein the step (a) includes the following steps (a1) to (a3): (a1) a rectangular waveguide having a reference length. For a microwave circuit having a tube (hereinafter referred to as a reference waveguide), E
When the relationship between the position of the plane stub and the circle center angle and the relationship between the position of the H plane stub and the circle center angle are measured in advance, and the E plane stub is fixed at a predetermined position and the H plane stub is moved. And the center angle of the circular locus (hereinafter, referred to as H reference phase) when the H plane stub is fixed at a predetermined position and the E plane stub is moved. (A2) In performing automatic tuning of a microwave circuit provided with a rectangular waveguide having an arbitrary length different from the reference waveguide, an E-plane of the microwave circuit is used. Stub,
When the H plane stub is moved while being fixed at the same position as the E plane stub when the E reference phase is obtained, the phase at the point where the absolute value of the reflection coefficient becomes substantially “1” (hereinafter referred to as E actual phase) )
When the E-plane stub is moved while the H-plane stub of the microwave circuit is fixed at the same position as the H-plane stub when the H reference phase is obtained, the absolute value of the reflection coefficient becomes substantially “1”.
And (a3) E-plane obtained for a microwave circuit provided with a reference waveguide by measuring at least one of the real phases. By correcting the relationship between the stub and the center angle of the circle by an angle corresponding to the difference between the E actual phase and the E reference phase, the E of the microwave circuit having the rectangular waveguide having the arbitrary length is corrected. Find the relationship between the plane stub and the circle center angle,
Similarly, by correcting the relationship between the H plane stub and the circle center angle obtained for the microwave circuit having the reference waveguide by an angle corresponding to the difference between the H actual phase and the H reference phase. Determining the relationship between the H-plane stub and the center angle of the circle of the microwave circuit having the rectangular waveguide having an arbitrary length; and the step (b) includes the following steps (b1) and (b2). (B1) a microwave circuit provided with a reference waveguide for at least one of the E reference phase and the H reference phase with respect to the microwave circuit provided with the reference waveguide; And (b2) automatically tuning a microwave circuit having a rectangular waveguide having an arbitrary length, wherein a displacement angle of a symmetric axis (hereinafter referred to as a reference symmetric axis) on the Smith chart is obtained in advance. You By subtracting the displacement angle of the reference symmetry axis from the actual phase corresponding to the reference phase when the displacement angle is obtained, the actual symmetry axis on the Smith chart of the microwave circuit (hereinafter, referred to as the “symbol axis”) is obtained.
In the step (c), a line symmetry point is obtained by using the real axis of symmetry obtained in the step (b2). In the step (f), a step (a3) is performed. The position of the E-plane stub is obtained using the corrected relationship between the E-plane stub and the circle center angle. In the step (g), the H corrected similarly in the step (a3)
An automatic tuning method for a microwave circuit, wherein a position of an H-plane stub is obtained using a relationship between a plane stub and a circle center angle. 4. The method according to claim 1, further comprising the following steps (4) to (7):
(4) After the positions of the E-plane stub and the H-plane stub are initially set by the processes (1) to (3), while controlling the positions of the two stubs in a direction in which the absolute value of the reflection coefficient becomes smaller, Monitoring the sudden change in the absolute value of the reflection coefficient during the operation of the wave circuit; and (5) detecting the sudden change in the absolute value of the reflection coefficient in the step (4). Then, the process of measuring the absolute value of the reflection coefficient and its phase at that time; and (6) the E-plane stub and the H-plane stub are both based on the measured absolute value of the reflection coefficient and its phase. A step of newly calculating the absolute value and the phase of the reflection coefficient when the stub is at the reference position; and (7) the steps (2) to (4) using the absolute value and the phase of the reflection coefficient obtained in the step (6). By performing step (3), Moving the E-plane stub and the H-plane stub to a position where impedance matching can be achieved. The step (6) is substantially the following steps (h) to (j): (h) the step (h) By referring to the relationship between the position of the E-plane stub and the center angle of the circle obtained in a) and the relationship between the position of the H-plane stub and the center angle of the circle, the E-plane when the reflection coefficient changes rapidly is obtained. A step of obtaining a circle center angle corresponding to the position of the stub and a circle center angle corresponding to the position of the H plane stub; and (i) a center of the circle corresponding to the position of the E plane stub obtained in the step (h). A point on the Smith chart that has an angle and is in contact with a circle whose absolute value of the reflection coefficient is “1” on the Smith chart and that corresponds to the absolute value of the reflection coefficient measured in step (5) and its phase A first circle passing through As described above, while having a circle center angle corresponding to the position of the H-plane stub obtained in the step (h) and touching a circle whose absolute value of the reflection coefficient is “1” on the Smith chart, A) determining the absolute value of the reflection coefficient measured in step 2) and a second circle passing through a point on the Smith chart corresponding to the phase thereof; and (j) two intersections of the first and second circles. With respect to the absolute value of the reflection coefficient measured in the process (5) and the other intersection on the Smith chart corresponding to the phase thereof, which is different from the one intersection, it is line-symmetric with respect to the symmetry axis obtained in the process (b). The impedance point on the Smith chart is obtained, and the E plane stub and H
A process for newly obtaining the absolute value of the reflection coefficient and its phase when both of the surface stubs are at the stub reference position; and a process for automatically tuning the microwave circuit. 5. The method according to claim 4, wherein the processing in the step (6) is performed by using the E determined in the step (a).
The absolute value of the reflection coefficient when the absolute value of the reflection coefficient sharply fluctuates, which is obtained based on the relationship between the position of the plane stub and the circle center angle, and the relationship between the position of the H plane stub and the circle center angle, and The phase and an approximate function relating the absolute value of the reflection coefficient when the E-plane stub and the H-plane stub are both at the stub reference position and the phase thereof have an E.sub. The center angle of the circle corresponding to the position of the plane stub, the center angle of the circle also corresponding to the position of the H plane stub, the absolute value of the reflection coefficient when the absolute value of the reflection coefficient fluctuates rapidly, and its phase are given. By performing the above steps (h) to (j) substantially,
An automatic tuning method for a microwave circuit, wherein an absolute value and a phase of a reflection coefficient when both an E-plane stub and an H-plane stub are at a stub reference position are obtained.